TI-82: Statistics Mode

1-Variable Statistics

There is one routine on the calculator, called 1-Variable Statistics which will find

• the sample mean
• the sum of the data values
• the sum of the squares of the data values
• the sample standard deviation
• the population standard deviation
• the sample size
• the minimum value
• the first quartile
• the median
• the third quartile
• the maximum value

It also saves all of these values to variables so they can be used in other calculations without having to re-enter the information.

Obtaining 1-Variable Statistics

1. Enter the data. If the raw data is used, it goes into one list only. If a frequency distribution is to be entered, then put the data values into one list and the corresponding frequency into another list.
2. Calculate the 1-Variable Statistics (STATS CALC 1)
3. Be sure to specify which list your data is in when you do the 1-Variable Statistics.

Examples

1-VAR STATS L₁

This will find the 1-Variable statistics for the data contained in list 1. Each element in list 1 is assumed to have a frequency of 1.

1-VAR STATS L₁,L₂

This will find the 1-Variable statistics for the data contained in list 1. Each element in list 1 is assumed to have a frequency of the corresponding element in list 2.

Using the 1-Variable Statistics

The results of the 1-Variable Statistics (and any other statistical calculations done later) are under the VARS key, menu choice number 5: STATISTICS. Go ahead and press that now "VARS 5"

Variance

Since the calculator gives the standard deviations instead of the variances, the first thing often found is the variance. The sample standard deviation is number 3 and the population standard deviation is number 4.

   VARS 5 3 x2     - sample variance
   VARS 5 4 x2     - population variance

Variation

The variation is used as a step in finding the variance and ultimately the standard deviation when calculating those values by hand. Since we are going to concentrate on understanding the statistics and letting the calculator concentrate on finding the statistics, we aren't going to use the variation very often.

One place that the variation will come into use is when we're working with Analysis of Variance (ANOVA). The total variation can be found by multiplying the degrees of freedom by the sample variance or the sample size by the population variance.

   ( VARS 5 1 - 1 ) * VARS 5 3 x2
   VARS 5 1 * VARS 5 4 x2

Standard Scores

The way to compute the z-score is to subtract the mean from each value and then divide by the standard deviation. Since the mean and standard deviation are stored in variables, you can use them in the formula directly. This expression will convert the entire list at once. If you wish to find the z-score for a single value, then replace the L1 with that value.

   ( L1 - Xbar ) / Sx

To generate the Xbar, press: VARS 5 2
To generate the Sx, press: VARS 5 3

Interquartile Range

The quartiles are stored under VARS STATISTICS(5) BOX.

   Q3 - Q1

or

   VARS 5 BOX 3 - VARS 5 BOX 1

Range

   MAXX - MINX

or

   VARS 5 9 - VARS 5 8

Midrange

   ( MAXX + MINX ) / 2

or

   ( VARS 5 9 - VARS 5 8 ) / 2

Cutoff for mild outliers

   Q1 - 1.5 * (Q3 - Q1)

and

   Q3 + 1.5 * (Q3 - Q1)

Cutoff for extreme outliers

   Q1 - 3 * (Q3 - Q1)

and

   Q3 + 3 * (Q3 - Q1)